MOST

**Mode**

Simply put...this is the

AVERAGE

**Mean**

Simply put...the

MIDDLE

when the data is arranged in order from least to greatest.

**Median**

Your soccer coach has been recording your shots on goal to help you get better. Below are the number of shots you took per game so far this season. Find the mean and mode.

Find the mean & mode

A group of 6th graders are working hard to turn their behavior around in the cafeteria. For the last two weeks Miss Christine has been keeping track of how many times someone from their team has to be talked to per day for their behavior. Her data is below. Find the median and range.

Find the Median & Range

On your first four math tests you earned a 85, 80, 95, and a 65 (hey, anyone can have a bad day). What must you earn on your next test to have a mean score of at least 80?

Challenge Card!

**Mean, Median, Mode & Range**

We use mean to:

figure out your grades

to give an overall impression of an action or the data

Keep in mind, the more data you have the less each number will change the average. The smaller the data set the more each number matters.

How to find the mean

1. Add up all the data

2. Divide the sum by the number of data used.

That is it!

Practice:

These are Griffin's math grades, what is his mean?

78, 90, 89, 82, 85, 94

78 + 90 + 89 + 82 + 85 + 94 = 518

518 divided by the number of grades (6) = 86.33...

You try it:

7, 5, 8, 9, 9, 3, 7, 10

what do you think would happen if we took out the 78 and replaced it with a 98?

7 + 5 + 8 + 9 + 9+ 3 + 7 + 10 = 58

58 / 8 = 7.25

Do you think 7.25 is a good representation of the data set?

Why or Why Not?

Turn to your partner and discuss

We use median to:

find the CENTER of the data

to describe data that may have a couple drastic changes, as median is not that influenced by a random number (or outlier) - like in a survey with a rating scale.

Practice:

Below are the results from a customer satisfaction survey where 10 customers were asked to rate their experience at the store from 1 - 9. Notice how most of the results are the same, but there is one "1" in the group.

7, 5, 6, 6, 5, 9, 6, 1, 7, 5

How to find the median

1. Arrange all the data in order from least to greatest.

2. Starting at the outside numbers, cross off one number from each side until you find the center number.

* If two numbers split the middle, you have to add them together and use their average (divide by 2).

1, 5, 5, 5, 6, 6, 6, 7, 7, 9

1. put the #s in order:

2. cross out a # end by end until you reach the CENTER #.

1, 5, 5, 5, 6, 6, 6, 7, 7, 9

3. If there are 2 numbers splitting the center - find the average of the two.

6 + 6 = 12 / 2 = 6

You try it:

(tip - it helps to cross off each number as you put it in order.)

4, 6, 7, 8, 9, 10, 3, 6, 7, 15, 2

the median - or center is...

7

We use the mode to:

find a trend

best when used with data that has categories.

FYI: this is the least used measurement.

How to find the mode:

1. Analyze the data

2. Determine which data value has the highest frequency (repeats the most).

Practice:

The following is the number of problems that Ms. Matty assigned for homework on 10 different days. What is the mode?

8, 11, 9, 14, 9, 15, 18, 6, 9, 10

Solution: Ordering the data from least to greatest, we get:

6, 8, 9, 9, 9, 10, 11 14, 15, 18

Answer: The mode is 9.

You try it!

The following are the number of points scored in a series of football games. What is the mode?

7, 3, 18, 24, 18, 24, 9

1. Put them in order from LEAST to GREATEST to avoid making a mistake.

3, 7, 9, 18, 18, 24, 24

2. Identify which number occurs most often.

Since both 18 and 24 happen the same number of times they are both the mode.

**Range**

Simply put...the difference between the lowest and the highest number in a set of data.

We use range to:

show how diverse (different) the results are in data.

Show if there is a major difference between data results. (for example, a teacher can use it to analyze test results)

How to Find the Range:

1. The easiest way to is to subtract the lowest number from the highest number in the set of data.

2. Sometimes you have to be careful not to miss a number, or if the data includes negative and positive numbers.

*You may want to write the data on a number line.

Practice:

Below are a sample of grades from our last math quiz.

14, 16, 16, 13, 15, 16, 10, 7, 6, 16, 6, 7

16 - 6 = 10, the range is 10.

You Try It!

On my summer road trip I kept track of the gas prices. What is the range as we drove to Florida?

$1.45, $2.75, $3.05, $1.55, $2.55

3.05

- 1.45

$1.60

1, 15, 20, 15, 7, 14, 13, 16

Which measurement is a better representation of the data? Why?

15, 10, 11, 13, 9, 6, 7, 4, 2, 2, 1, 1, 3, 1

Are these good measurements of the data? Will the range and median be helpful for the Mrs. Bull to see that the 6th graders are doing better? Why or why not?

Think about how many scores you will have in the end? What is the lowest sum you can have and then divide by the number of scores and still achieve your goal?

HINT: